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The goal of this chapter is to review recent analytical results about the growth of a (static) correlation length in glassy systems, and the connection that can be made between this lengthscale and the equilibrium correlation time of its dynamics. The definition of such a lengthscale is first given in a generic setting, including finite-dimensional models, along with rigorous bounds linking it to the correlation time. We then present some particular cases (finite connectivity mean-field models, and Kac limit of finite-dimensional systems) where this length can be actually computed.

The goal of this chapter is to review recent analytical results about the growth of a (static) correlation length in glassy systems, and the connection that can be made between this lengthscale and the equilibrium correlation time of its dynamics. The definition of such a lengthscale is first given in a generic setting, including finite-dimensional models, along with rigorous bounds linking it to the correlation time. We then present some particular cases (finite connectivity mean-field models, and Kac limit of finite-dimensional systems) where this length can be actually computed.